Lab meeting

Bob Week

03/10/21

The Signature of Coevolution
in Continuous Space

https://doi.org/10.1016/B978-0-12-800049-6.00188-8

Motivation

  • Space has long been thought to play a crucial role in the coevolutionary process

    • Local adaptation and gene-flow may lead to patterns of trait mismatch and maladaptation

  • Past theoretical work has largely ignored the relationship between coevolution and IBD

    • This is particularly troublesome for methods seeking to identify coevolving loci

  • Here we outline three projects that attempt to answer the following questions

Questions

  • At what spatial scales do interspecific coevolutionary patterns emerge?

    • The spatial scale of interspecific trait/genotype cross-correlations?

  • How does this relate to spatial scales of intraspecific local adaptation?

    • How can we measure local adaptation?

  • How do these spatial scales and their relationships depend on dispersal distances and environmental heterogeneity?

  • Can we disentangle the signature of coevolutionary adaptation from isolation by distance?

Outline

  • We focus on host-parasite coevolution

  • Three projects:

    1. Phenotypic

    2. Two-locus

    3. SLiM

Phenotypic

This initial project seeks to answer questions relating to spatial scales of coevolution, local adaptation and environmental heterogeneity using a quantitative-genetic model. By focusing on phenotypic evolution, we may obtain a more broadscale understanding of these phenomena before diving into genetic/genomic details.

Two-locus

This project injects further genetic details by modeling coevolution mediated by two loci in each species. This allows comparisons of intraspecific linkage-disequilibrium to interspecific linkage-disequilibrium, thereby creating the opportunity to distinguish between interspecific linkage due to IBD and coevolution.

SLiM

This project injects even further genetic details using genome-wide slimulations. Using these individual-based, genome-wide slimulations, we can test conclusions drawn from the simpler, but less realistic approaches taken above to see what we can expect to hold in the wild.

Phenotypic

Outline of Model

  • Species \(H\) and \(P\)

  • Fitness \(m_H,m_P\) determined by quantitative traits \(z_H,z_P\)

  • Assuming individuals encounter each other at random, mean fitness \(\bar m_H,\bar m_P\) calculated by averaging across \(z_H,z_P\)

  • Mean trait dynamics given by

    • \(\frac{d}{dt}\bar z_H=G_H\beta_H+\xi_H\)

    • \(\frac{d}{dt}\bar z_P=G_P\beta_P+\xi_P\)

    • \(G_H,G_P\) are additive genetic variances

    • \(\beta_H,\beta_P\) are selection gradients \(\left(=\frac{\partial\bar m_H}{\partial\bar z_H},\frac{\partial\bar m_P}{\partial\bar z_P}\right)\)

    • \(\xi_H,\xi_P\) are random processes capturing drift

Trait-matching

Coevolutionary Dynamics
(non-spatial)

Trait Dynamics

Adding Space

  • Can use theory of random fields to get spatial (intraspecific) correlation and (interspecific) cross-correlation functions.

Spatial Correlation Functions

\(D_H,D_P=\) host/parasite dispersal distance

\(\rho_H,\rho_P,\rho_{HP}=\) spatial (cross)-correlations

  • Q: What can we conclude from this figure?

Measuring Local Adapation

  • We have fitness functions \(m_H(z_H,z_P),m_P(z_P,z_H)\)

  • So we can calculate difference in fitness for

    • local interactions (home) vs
    • interactions at a spatial lag (away)

  • \(\Delta_H=\mathbb E[m_H(z_H(x),z_P(x))-m_H(z_H(x),z_P(y))]\)

    • \(x,y=\) spatial locations

Local Adaptation

TODO

  • implement environmental heterogeneity

    • random field (for clumpiness)

    • clines (linear=easy, but should we do more?)

People to invite

Sally Aitken (left) local adaptation, tree genomics
Tanja Stadler (right) coalescent theory, phylogenetics